Physics with Elliot
Physics with Elliot
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How Feynman did quantum mechanics (and you should too)
Discover Feynman's path integral formulation of quantum mechanics! 📝 Get the notes for free here: courses.physicswithelliot.com/notes-sign-up
👨‍🏫 Enroll in my course on Lagrangian mechanics!
bit.ly/lagrangian-fundamentals
✉️ Sign up for my newsletter for additional physics lessons: www.physicswithelliot.com/sign-up
📺 My previous video about the double-slit experiment and wavefunctions:
czcams.com/video/Se-CpexiJLQ/video.html
📺 My earlier video about the principle of least action:
czcams.com/video/sUk9y23FPHk/video.html
🅿 Become a patron to help make videos like these possible:
www.Patreon.com/PhysicsWithElliot
🙋‍♀️ "What software did you use to make this video?" and other FAQs:
www.physicswithelliot.com/faq
⚛️ Additional links:
- Feynman's 1964 lecture on quantum mechanics:
www.feynmanlectures.caltech.edu/fml.html#6
- Feynman's PhD dissertation can be found in this book:
www.worldscientific.com/worldscibooks/10.1142/5852#t=aboutBook
- Feynman's original paper on the path integral:
authors.library.caltech.edu/records/9h858-5hv71
- Dirac's 1932 paper that inspired Feynman:
www.worldscientific.com/doi/10.1142/9789812567635_0003
- Feynman's Nobel lecture, including the origin story of the path integral:
www.nobelprize.org/prizes/physics/1965/feynman/lecture/
- Feynman and Hibbs's textbook "Quantum Mechanics and Path Integrals" from the 1960s:
books.google.com/books/about/Quantum_Mechanics_and_Path_Integrals.html?id=JkMuDAAAQBAJ
📖 Video summary:
If you've learned some quantum mechanics before, you've probably seen it described using wavefunctions, and the Schrödinger equation, and so on. That's how quantum mechanics was originally constructed by people like Schrödinger, Born, Heisenberg, and many others in the 1920s.
In the 1940s, though, a 20-something-year-old grad student named Richard Feynman discovered another approach. He found that the motion of a quantum particle can be described by taking a sum over ALL the possible trajectories that the particle could conceivably follow. That sum over all quantum paths is what's nowadays called the Feynman path integral, and it's central to our modern understanding of quantum physics.
One of the most important lessons Feynman's perspective reveals is how the usual laws of classical mechanics emerge from this more fundamental, but seemingly very different, quantum mechanical description of nature. In the video, you'll see why a single, special path emerges from the sea of all possible quantum paths when we consider the motion of a big object like a baseball--called the path of stationary action. And that of course is the path that obeys F = ma!
0:00 Introduction
3:12 Quick overview of the path integral
5:46 Review of the double-slit experiment
8:32 Intuitive idea of Feynman's sum over paths
13:27 Why exp(iS/hbar)?
15:00 How F = ma emerges from quantum mechanics
23:15 Lagrangian mechanics
24:34 Feynman's story
25:22 Next time: how to compute the path integral?
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at www.Patreon.com/PhysicsWithElliot, or make a one time contribution at www.physicswithelliot.com/support-me. Thank you so much!
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com.
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Komentáře

  • @alphamf0
    @alphamf0 Před 4 hodinami

    What app do you use to write?

  • @tomekgwozdz6037
    @tomekgwozdz6037 Před 9 hodinami

    Rings with all nonzero elemnts invertable go brrrrrrrr

  • @mcqueen424
    @mcqueen424 Před dnem

    Replace Laplace transform with Fourier transform and your video might actually be good

  • @kisho2679
    @kisho2679 Před dnem

    But isn't the real challenge in finding the potential energy in a specific problem?

  • @FLORIDIANMILLIONAIRE

    Just do static analysis and oversizing comes with experience dont need differential equations

  • @mohammedseid1987
    @mohammedseid1987 Před 2 dny

    0-0

  • @SubEthaEngineer
    @SubEthaEngineer Před 2 dny

    i love you

  • @SubEthaEngineer
    @SubEthaEngineer Před 2 dny

    beautiful! thank you for making this

  • @RickGGb1
    @RickGGb1 Před 2 dny

    I wish my professors were this good at explaining

  • @kk12181
    @kk12181 Před 2 dny

    Why should we take 2nd derivative??

  • @chucky428
    @chucky428 Před 2 dny

    great remedy of insomnia

  • @FB0102
    @FB0102 Před 3 dny

    Can you explain why the standard Lagrangian is T-U? Intuitively, why that specific form (other than 'because it works')? Thanks

  • @captaingenyus843
    @captaingenyus843 Před 3 dny

    Thats just fcking great!

  • @PHY-easy-ICS
    @PHY-easy-ICS Před 4 dny

    One of the best explanations on this topic

  • @agrajyadav2951
    @agrajyadav2951 Před 4 dny

    Thanks a lot, sir!

  • @al8188
    @al8188 Před 4 dny

    "There's a good chance you've run into this equation before." My man, its 11PM and I'm eating a donut on my kitchen counter. Not only have I not run into that equation before, but in an hour it is going to be replaced with more math I can't do, a video about a cool rock, or documentary about a country I ain't ever gonna go to. Simple Harmonic Oscillators look like they kick all kinds of ass but I am up too late looking for answers to problems that differential equations can't solve. Do not underestimate how dumb I am.

  • @CeRz
    @CeRz Před 5 dny

    Here before this channel gets millions and millions of subscribers. Keep doing these animations, they are invaluable when you show the concepts. It really helps visualising the physics and the math.

  • @PhysicsNg
    @PhysicsNg Před 6 dny

    My teacher said I dont need to study lagrangian until I can get into APhO😂

  • @user-uc8nz8io2k
    @user-uc8nz8io2k Před 8 dny

    E=mc^2 Schwarzschild radius

  • @nychan2939
    @nychan2939 Před 8 dny

    It seems I can win Nobel prize if I take your course.

  • @zord1352
    @zord1352 Před 9 dny

    I have just found this channel, weeks before QM exams. Your videos really helps to patch the fragments. Thank you the video!

  • @jaxetika
    @jaxetika Před 9 dny

    Anyone else still have no clue?

  • @robyn-lee-INFJ
    @robyn-lee-INFJ Před 9 dny

    Probability of finding an orgasm in Ex

  • @UdiDol
    @UdiDol Před 10 dny

    Great1

  • @liadvazina6027
    @liadvazina6027 Před 10 dny

    im starting quantum theory 1 now and the next video could really help!

  • @asdf7219
    @asdf7219 Před 10 dny

    Wolframalpha

  • @liltike2197
    @liltike2197 Před 10 dny

    The only problem is that the hamiltonian is not always equal to the total energy.

  • @CandidDate
    @CandidDate Před 11 dny

    What are you talking about?

  • @asdf7219
    @asdf7219 Před 11 dny

    Why do we use dot notation to regard n-th order differentials instead of the standard apostrophe "prime" such as f'(x)?

  • @takyon24
    @takyon24 Před 11 dny

    Man this is high quality, easy some of the best physics educational content on youtube. Do you still plan on uploading any problem sets for this video? Thanks a lot for the notes btw

  • @CandidDate
    @CandidDate Před 11 dny

    You got to be some kind of big idiot to be surprised still how nature works!

  • @jordansimmons2748
    @jordansimmons2748 Před 11 dny

    This just made my head hurt

  • @jiukam
    @jiukam Před 12 dny

    Im fking enlightened

  • @n_fieldgaming
    @n_fieldgaming Před 12 dny

    Thank you so much sir for this video ❤✨

  • @jayhariyani5361
    @jayhariyani5361 Před 12 dny

    Why normalised wf is required??

    • @lepidoptera9337
      @lepidoptera9337 Před 7 dny

      It isn't, really. The normalization is merely an expression that we are dealing with an ensemble (i.e. an infinite repetition of the same experiment). It works well for closed systems with finite volume and it doesn't work, at all, for scattering problems. It's kind of the toy version of the real theory.

  • @thestickdog3621
    @thestickdog3621 Před 12 dny

    ah, yes, one of the most known engineering theorems: sin T = T

  • @MuhammadRamzan-tf6br
    @MuhammadRamzan-tf6br Před 12 dny

    Amazing, thank you so much. It was music to the ears listening to you!

  • @fikaduzawdie3677
    @fikaduzawdie3677 Před 13 dny

    MashaAllah

  • @dhwang101
    @dhwang101 Před 14 dny

    So... You don't need calculus unless you want to find a particle. Ok, wasted a year in school 😂😂😂

  • @olivierbarbe9269
    @olivierbarbe9269 Před 14 dny

    Great video thanks, very clear and engaging

  • @ggxsky4811
    @ggxsky4811 Před 14 dny

    Lagrangian is sick

  • @JeromeCallas
    @JeromeCallas Před 14 dny

    I'm gonna do u the good of telling u why I can't hang: u called Newton's interpretation of his share of facts "nonsense", as if u with the same facts could've done better. Look up the words "intellectual" and "hubris", then have a think.

  • @sensorer
    @sensorer Před 16 dny

    Hate to be a hater, but I find the explanation in this video to be lacking and circular. Okay, so we're going to pull out this factor (1/ih_bar) and this here is a quantum generator(because it just is), and now that we've pulled out of our hat that it's the quantum generator, it should be momentum. For me, Dirac's approach of getting the quantum Poisson bracket from the classical one is much more satisfying and then using the canonical commutation relations you got from that you find the translation operator and all the other stuff you want.

  • @user-ej5cd4ei2l
    @user-ej5cd4ei2l Před 17 dny

    On a xyz graph, a point is potential energy. Time is kinetic energy when going to another point. This existence is amplitude and is nested between another reality made up of shattered pieces.

  • @SampleroftheMultiverse

    Thanks for your interesting article. My intuition said there is something important about this mechanical effect. This model shows how a field represented by a sheet of elastic material under the right initial conditions naturally form quantized energy levels. From there it was easy to form very stable three dimensional structures using a very minimal amount of material. (similar to the way engineers built large light weight space structures) czcams.com/video/wrBsqiE0vG4/video.htmlsi=waT8lY2iX-wJdjO3 You and your followers might find the quantum-like analog useful in visualize nature properties of fields. I have been trying to describe the “U” shape wave that is produced in my amateur science mechanical model in the video link. I hear if you over-lap all the waves together using Fournier Transforms, it may make a “U” shape or square wave. Can this be correct representation Feynman Path Integrals? In the model, “U” shape waves are produced as the loading increases and just before the wave-like function shifts to the next higher energy level. Your followers might be interested in seeing the load verse deflection graph in white paper found elsewhere on my CZcams channel. Actually replicating it with a sheet of clear folder plastic and tape and seeing it first hand is worth the effort.

  • @michaelzap8528
    @michaelzap8528 Před 19 dny

    Oh my God, heroes see the same thing. When I decided to teach my son physics, the first thing I did was teach him solar system, Euler's formula, the Fourier transform, basically the circle.

  • @jordanfreidel1751
    @jordanfreidel1751 Před 20 dny

    Why can’t I use sin theta in the final equation? Or does it not make a difference, or am I just blind and short circuiting when doing the second derivative?

    • @robert.ehrlich8942
      @robert.ehrlich8942 Před 16 dny

      There is something missing at this stage in the video. After saying that cos theta or sin theta are solution of the equation without the "1", he keeps only the cos variant without further explanation. For such linear equations, any linear combination of solutions is also a solution, so the general solution would be A cos theta + B sin theta. Not surprising, a second order differential equation usually depends on 2 integration constants. This can be rewritten as C cos (theta - phi) with the two new constants C = sqrt(A²+B²) and phi = atan(B/A). In the following he assumes that phi = 0, which can always be obtained by rotating the x,y axes by phi, so eliminating one of the two constants. This is why all the following trajectories are symetrical relatively to the x axis, which is not implied by the initial description of the problem.

    • @jordanfreidel1751
      @jordanfreidel1751 Před 16 dny

      @@robert.ehrlich8942 then that would mean that using sin theta would be an acceptable answer correct?

  • @ravikantpatil3398
    @ravikantpatil3398 Před 23 dny

    Great explained thanx

  • @vernonmeidlinger870
    @vernonmeidlinger870 Před 23 dny

    I'm so grateful for this video. I've been trying to self-study Differential Equations and kept getting stuck early on. This really helped clarify not only what to do to solve Differential Equations but WHY the methods work. Thank you!

  • @Karlswebb
    @Karlswebb Před 24 dny

    Symmetry groups are the universe. The universe, in my view, a mathematical truth/structure. It (reality) is what happens when you have these mathematical objects called quantum fields defined on a manifold (spacetime) in some type of initial ordered/low entropy state. In theory all possible self consistent mathematical structures exist, so a structure with interacting quantum fields defined on a manifold with more than 3 spatial dimensions can’t exist as any interactions in 4 or more spatial dimensions lead to non-renormalizability, meaning the math becomes nonsensical and inconsistent so it can’t occur. But one in 2 spatial dimensions probably could, in 3 or less spatial dimensions qft’s can be interacting and renormalizable (meaning they are predictive).